Suppose we have $f(x)=x$; and $g(x)=x^2$.
We know that $x$ and $x^2$ intersect at $(1,1)$. How to make a function $h$ that equals $f$ on $[0,1]$ and equals $g$ on $[1,\infty)$?
What will be the function $h(x)$ (for example) ?
double function combination
1
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functions
graphing-functions
1 Answers
1
We can get $h(x)$ as function defined for cases: $$h(x)=\begin{cases}-x^2\hspace{0,7cm}(-\infty,0)\\x\hspace{1,3cm} [0,1)\\x^2\hspace{1,1cm} [1,+\infty) \end{cases}$$
This is a continuous function for $x\in\mathbb R$, because $e(x)=-x^2$, $f(x)=x$ and $g(x)=x^2$ are continuos functions and $e(0)=f(0)=0$, $f(1)=g(1)=1$, thus they "stick" together to $x=0$ and $x=1$.